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A function f (x) is defined as f (x) = x + a, x < 0 = x, 0 ≤x ≤ 1 = b- x,   x ≥1 is continuous in its domain. Find a + b. - Mathematics and Statistics

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A function f (x) is defined as
f (x) = x + a, x < 0
= x,       0 ≤x ≤ 1
= b- x,   x ≥1
is continuous in its domain.
Find a + b.

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Solution

f (x) is continuous in its domain.

f (x) is continuous at x = 0 & x = 1
Since f(x) is continuous at x = 0

`therefore lim_(x->0^-)f(x)=lim_(x->0^+)f(x)=f(0)`

`lim_(x->0)(x+a)=lim_(x->0)x=0`

`0+a=0`

`a=0`

Also f (x) is continuous at x = 1

`therefore lim_(x->1^-)f(x)=lim_(x->1^+)f(x)=f(1)`

`lim_(x->1)(x+a)=lim_(x->1)(b-x)=b-1`

`1=b-1`

`b=2`

`a+b=2`

Concept: Algebra of Continuous Functions
  Is there an error in this question or solution?

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